A layer of a silicon germanium alloy containing 30 atomic percent or greater germanium and containing substitutional carbon is grown on a surface of a semiconductor layer. The presence of the substitutional carbon in the layer of silicon germanium alloy compensates the strain of the silicon germanium alloy, and suppresses defect formation. Placeholder semiconductor fins are then formed to a desired dimension within the layer of silicon germanium alloy and the semiconductor layer. The placeholder semiconductor fins will relax for the most part, while maintaining strain in a lengthwise direction. An anneal is then performed which may either remove the substitutional carbon from each placeholder semiconductor fin or move the substitutional carbon into interstitial sites within the lattice of the silicon germanium alloy. Free-standing permanent semiconductor fins containing 30 atomic percent or greater germanium, and strain in the lengthwise direction are provided.